Answer:
a) The astronauts would see the real length of the meter stick, i.e. L₀
b) The length of the meter stick as measured by the stationary observer will be [tex]L = L_{0} }{\sqrt{(1-(\frac{v}{c} )^{2} } }[/tex]
Explanation:
a) Let the proper length of the meter stick be L₀
The meter stick and the astronauts on the on the space ship are on the same moving frame, therefore, they will see the exact length of the meter stick, that is, L₀
b) A stationary observer watching the space ship and meter stick travel past them will see a contracted length of the meter stick
The original length = L₀
Let the speed of the space ship = v
The contracted length, L, is related to the original length in the frame of rest by
L = L₀/γ......................(1)
Where γ = [tex]\frac{1}{\sqrt{(1-(\frac{v}{c} )^{2} } }[/tex] ....................(2)
Substituting equation (2) into (1)
[tex]L = L_{0} }{\sqrt{(1-(\frac{v}{c} )^{2} } }[/tex]
